TRB ANNUAL MEETING 2016
A New Model for Aircraft Cost Index Calculation
Holly Edwards*, Doctoral Training Centre in Low Carbon Technologies, University of Leeds,
Leeds, LS2 9JT, UK, Tel: +447875531114, E: [email protected]
Darron Dixon-Hardy, Energy Research Institute, University of Leeds, Leeds, LS2 9JT, UK, Tel:
+44113 3432800, E: [email protected]
Zia Wadud, Centre for Integrated Energy Research and Institute of Transport Studies, University of
Leeds, Leeds, LS2 9JT, UK, Tel: +44113 34 37733, E: [email protected]
*Corresponding Author
1 August 2015
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
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ABSTRACT
The cost index (CI) is a tool that is growing in importance for airlines. It works by balancing the costs
of time with the cost of fuel to determine the speed of a flight. Slower speeds result in fuel cost
savings but higher time-dependent costs and faster flights vice versa. With the cost of fuel rising and
climate change issues surrounding air travel increasing the need for efficiency, the CI needs to be
optimised. However, in general airlines find the calculation of CI challenging, particularly regarding
extra costs owing to delay and cumulative maintenance and crew costs. The aim of this paper is to
present a new way of calculating CI values on a flight-to-flight basis through the optimised cost index
(OCI) model. Instead of constraining all costs to the traditional CI equation, the OCI model uses
additional alternative calculations to take all costs into account fully. The OCI model provides an
accessible and transparent way of calculating optimum CI values for airlines through a simple
interface. In the future the model can also be used to assess the impact of future policies on a flight-toflight basis, adding extra value to the OCI model.
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
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2
INTRODUCTION
The cost index (CI) has been available in most commercial aircraft since the 1970s, with the purpose
of controlling the speed of aircraft in order to minimise operational costs. Fuel costs have increasingly
become one of the largest costs to airlines, accounting for 32% of global airline operating expenses in
2014, which is five times higher than in 2003 [1], suggesting an impetus to optimise flight operations
in favour of lower fuel use. One of the easiest ways to do this is to reduce the speed of a flight.
However, fuel is not the only cost needing to be considered, as slower flights can also increase other
costs. Time-dependent costs include crew costs and maintenance, which are paid by the flight hour
and increase with slower aircraft speeds. In the case of delay, time-dependent costs associated with
passenger compensation also become important.
The CI represents the cost per unit of time divided by the cost per unit of fuel, for a specific
flight. The resulting value is supplied to the pilot in the briefing package, who enters it into the Flight
Management Computer (FMC) prior to departure. As CI values are determined in advance, the FMC
will automatically calculate the final flight profile by adjusting the figure to incorporate conditions for
that particular flight, such as wind speed and altitude. CI values range from zero at Maximum Range
Cruise (MRC) where fuel costs are minimised, to a value corresponding to the highest possible
aircraft speed, where time-dependent costs are minimised.
As well as flight time and fuel use, the CI ultimately determines the CO2 emissions on a
flight-by-flight basis, which are directly proportional to the amount of fuel used. Aviation emissions
currently account for 3% of global CO2 emissions, but with an annual average increase in demand for
air travel of 5%, these emissions are set to represent a much greater proportion of global emissions in
the future. With limited large-scale technological solutions, the industry is reliant on a basket of
smaller measures to combat increases in emissions. The CI could be a valuable contributor to these
measures if its use can be optimised.
Limited research exists on the optimisation of CI for normal operations, especially in terms of
its effect on fuel use and CO2 emissions. Two early studies relating the CI to fuel use savings are
Liden [2] and Dejonge and Syblon [3]. More recent studies have looked at the issue of fuel use and
the speed of the aircraft but have principally addressed the problem from the delay recovery point of
view [4, 5].
Cook et al. [6] have undertaken the most comprehensive work regarding the CI and have
produced one of the few studies to include environmental impacts in their analysis. The study focuses
on creating a dynamic CI tool to help with delay recovery. The inclusion of an environmental decision
tool and an environmental signature acknowledges that the “political position relating to emission
charges is uncertain therefore a flexible framework” is needed to ensure that the dynamic CI stays
relevant in the decision making process in response to delay.
A previous study by the authors [7] shows the importance of CI in determining emissions on a
flight-by-flight basis by comparing fuel burn and flight time of six different aircraft models over six
different distances (Figure 1) . When aircraft are flown at their design range the difference between
the maximum CI and MRC, an average of 1% emissions saving can be made, with as much as a 3.9%
change in CO2 emissions for the A380-800. This may seem small but if 1% of the global CO2
emissions from aviation of 705,000,000 tonnes were reduced, this would be equivalent to the CO2
emissions of around 1000 long-haul flights. This also represents a saving of in the global aviation fuel
bill of around $2 billion a year. As aircraft are already equipped with the cost index tool, there are
only small monetary and time costs involved in implementing changes.
Although it is generally accepted that aircraft fly at their Long Range Cruise (LRC) speed –
one in which a 1% penalty in fuel consumption is sacrificed for a faster flight time – research by
Lovegren and Hansman [8] shows that this is not always the case and in fact a large number of aircraft
fly above these speeds and a 1.6% saving could be achieved by moving to flying at LRC, with a 2.4%
for optimisation to MRC speed.
But there are significant gaps in the research regarding the value and optimisation of CI. Most
studies focus on delay recovery, but CI is also important for normal operations in determining the
optimal speed of the aircraft. Although there is consensus that CI is a useful tool there has been little
work on how to optimise it in a practical way for airline use and address issues with its calculation.
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
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The aim of this paper is to demonstrate how CI can be optimised using a newly created
optimised cost index (OCI) model taking into account the current difficulties in CI calculation by
airlines. Section 2 evaluates the issues that exist with the current use of CI, justifying the need for a
new model and Section 3 outlines the setup of the OCI model created by the authors. Section 4
discusses the results of a sensitivity analysis using the model and Section 5 discusses its practical use
within the airline industry, as well as areas for future research.
2
ISSUES WITH EXISTING COST INDEX
Two issues can arise with the use of CI; incorrect use and/or miscalculating the costs associated with
the CI equation. Airlines have been reported to use CI to approximate the Long Range Cruise (LRC) this where a 1% penalty in fuel consumption is taken in exchange for a faster flight time; adjustment
to higher CI values if necessary for schedule regardless of the associated fuel costs; calculating a
speed just below LRC; meeting schedule requirements; adoption of CI values from other aircraft
models; and adapting speed requirements only [9].
Airlines are often hindered by the complication of apportioning costs for the CI equation. Fuel
costs are the most volatile aspect of the calculation and CI values need readjustment regularly to take
changes into account. However, the difficulties associated with time costs are more fundamental.
Evidence suggests that many airlines make elementary errors in this area or make questionable
assumptions, such as assuming that maintenance costs owing to flight hours are 50% of total
maintenance costs [10].
Crew labour costs cause problems in determining the optimum CI as they can vary
significantly depending on the country of operation, the type of operation and the size of the aircraft
[11]. There are also issues with estimating costs for relief pilots, overtime payments and rest hours
required between flights [10, 12]. These latter issues are complicated by the need to determine them
over a period of time e.g. a month or a year, not just one flight. Faster flight times can reduce the
amount of rest times need and may avoid the need for reinforced crews, but conversely slower speeds
eventually lead to block hour increases to the extent that additional crew need to be recruited [10].
The other key component of time cost is maintenance. The principle time-dependent costs
arising include engine components and the labour intensive nature of checks required at certain flight
time intervals. As these checks take place over a number of years marginal costs needs to be based on
a total five year maintenance program [10]. Difficulties differentiating from flight cycle costs from
flight hour costs creates a significant barrier to accurate costing [10, 13]. In addition, maturity of the
aircraft also needs to be taken into account, as this has a significant impact on the cost of aircraft
maintenance at a given time [14].
Once time-dependent costs are correctly calculated, they should not significantly change over
time as they are under the control of the airline, unlike fuel costs, which can change rapidly. A caveat
to this is the occasional change to these costs from external sources. For example, in 2013 the
European Parliament implemented new aircrew fatigue legislation. Maximum flight duty time was
decreased by 45 minutes for pilots on night flights, as well as the maximum number of flight hours in
a 12 month period [15]. This results in increased pressure on scheduling crews and may require either
more overtime payments or the addition of extra relief crews, adding to the issue of cumulative costs.
In the case of delay, resulting passenger costs also need to be accounted for in the CI
calculation, which are divided into hard and soft costs. Hard costs include actual bottom line costs to
the airline from rebooking passengers onto other flights if connections are missed and providing
compensation. Soft costs mainly concern a loss of market share owing to passenger dissatisfaction. In
theory hard costs should be easier for airlines to calculate, but this is generally not the case as the data
involved can be very complex. Soft costs are understandably difficult to calculate as they rely on a
number of assumptions and on market conditions [6].
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
Figure 1: The relationship between fuel burn and flight time for six aircraft models over six distances with data
points representing individual CI values. Note: A300-600 unable to fly at distances over 3000nm [7].
4
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
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Aktürk et al. [4] adds that the current standard CI does not fully capture the flexibility of
controllable flight times and even in the area where there has been the most research, delay
management, optimisation decision support tools are still at the early stage of implementation at major
airlines.
Encouraging airlines to optimise their use of CI may be a considerable challenge. Airbus [9,
pp.8] states that “the mere fact that fuel costs can significantly vary from one sector to another
throughout the year should prompt airlines to consider adopting different cost indices for their various
routes”. However, this appears not to be the case and it is added that operations departments struggle
to persuade airline financial analysts to assess marginal operating costs, probably as they have not
understood the importance of the CI, which is still a largely unknown concept to their decision
makers.
Burrows et al. [10, pp.282] backs up these assertions stating that the CI is “an accounting
innovation which has been developed by largely non-accountants”, resulting in airlines failing to
exploit the full economic potential of CI. Simulations of CI calculations by Burrows et al. [10]
indicate that there is sufficient sensitivity of ECON speed to change in input variables and the misspecifying of variables produces sub-optimal speeds.
Given the issues that have been discussed it is evident that there are two key areas that need to
be addressed in terms of providing a new model for calculation of CI values. Firstly it needs to be
shown that improved CI values can be calculated in a simple and cost effective way and secondly that
the problems with calculation of costs can be overcome.
3
CREATING THE OCI MODEL
The OCI model is created with the aim of providing an easy to use interface to calculate CI values
initially using the CI calculation and then adjusting for addition costs and schedule restrictions. Figure
2 presents the processes involved in the OCI model. Produced using Excel, the basic premise of the
model is to avoid constraining all costs to the traditional CI equation, but to instead use additional
calculations to determine the optimum CI value. The model is set up in such a way that the CI is
calculated on a flight-by-flight basis, taking into account the specific aircraft, flight characteristics for
that day and up-to-date costing information.
From the airlines perspective the model should be easy to use on a day-to-day basis. The interface
page requires simple inputs about the flight that should be known to the airline’s operation department
and the only page of the model they should have to use on a regular basis. These inputs are:
1. Flight No. – linked by a dropdown list to the flight database page.
2. Aircraft Code – a dropdown list is used to pinpoint the specific aircraft in the maintenance
database. Even for the same model, different aircraft will have varying maintenance costs
depending on age and number of hours already flown for the month is question.
3. Average Wind Speed – represents the average wind speed in knots excepted for the flight in
question.
4. Crew Members – a drop down list of crew members linked to the crew database.
5. Cargo Weight –weight of cargo being carried on the flight that is linked to the Flight Data.
6. Number of Passengers – total number which is linked to the Flight Data.
7. Expected Delay – this can include the number the minutes of expected delay for an aircraft by
either regular holding time at the destination airport or unexpected delay owing to factors,
such as weather and maintenance problems.
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
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8. Connecting Passengers – this requires the number of passengers for each class that are
connecting for each onward flight to be entered. This will be linked to delay costs.
Once all of these inputs have been entered the user can then press the calculate button. The optimal CI
is displayed from the calculation page in both kg/min and 100lb/hour as different flight management
systems use different units. The corresponding Mach number, flight time, fuel use and emissions of
CO2, NOX, hydrocarbon and carbon monoxide emissions are also displayed.
Figure 2: Cost Index Model Processes
Inputs are linked to eight other worksheets representing the individual aspects of the cost calculation.
These should only need to be sporadically updated by the airline. The first worksheet compiles the
crew costs for all flight and cabin crew of the airline. As well as basic salary information, the number
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
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of hours already flown for the month and number of hours remaining are presented. In order to take
account of cumulative crew costs the time available for the flight in question is calculated by the
flights already flown and the scheduled time for the flights remaining (Equation 1).
𝑇𝐹 = (𝑇𝑀 − 𝑇𝐹 ) − 𝑇𝑅
[1]
Where:
TF = Time available for the flight in question
TM = Maximum time available per month for crew member before overtime
TF = Time already flown this month by crew member
TR = Time needed for other flights remaining to be flown this month
The maintenance costs worksheet works in a similar way with each aircraft in the fleet being available
for the user to choose from a dropdown list on the interface page. Information is held on each aircraft
for time-dependent maintenance costs and hours flown in the given month. Also if the aircraft is under
a maintenance contract then the contracted hours and the hours remaining on that contract are also
included.
The fuel worksheet contains the spot price of jet fuel taken from the interface page along with
the percentage of fuel that is hedged and the hedging price. It is anticipated that the latter two will
need occasional adjustments by the airline but not as regularly as the spot price of fuel, therefore are
not included on the interface page. The other fuel related cost included here is the carbon price, if
applicable, which is proportional to the amount of fuel used. The total fuel costs are calculated from
Equation 2.
𝐹𝐶 = (%𝐹𝐻 ∗ 𝐹𝐻𝑃 ) + (%𝐹𝑆 ∗ 𝐹𝑆𝑃 ) + 𝐶𝑃
[2]
Where:
FC = Fuel Cost ($/kg)
%FH = % of jet fuel that is hedged
FHP = Jet fuel hedge price ($/kg)
%FS = % of jet fuel that is not hedged and subject to the spot price
FSP = Jet fuel spot price ($/kg)
CP = Carbon price ($/kg)
There are three types of passenger delay costs that need to be taken into account (Figure 3). The
simplest calculation is for those passengers not connecting to other flights. These passengers will be
owed compensation (depending on the country in which the flight arrives) if the flight is later than a
defined period e.g. 3 hours. Connecting passengers will need to be rebooked onto other flights if they
miss them owing to delay of the original flight, as well as any compensation if their final flight arrives
after the defined period. The third does not concern passengers of the original flight, but the
passengers on the succeeding flight by the same aircraft. In this case help and care costs i.e. meal
vouchers, phone cards etc. are required to be paid if the aircraft is late departing. These are again only
payable after a certain period of time and depend in part on the minimum time that the aircraft can be
turned around in.
Compensation costs are calculated by multiplying the number of passengers by the amount of
compensation if the delay exceeds a certain period of time. For example in the EU there are different
categories of compensation for short-, medium- and long-haul flights with the minimum delay period
being three hours before passengers are entitled to this compensation.
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
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Figure 3: Passenger Delay Costs
For care costs the minimum turnaround time for the aircraft is taken from the actual time between the
two flights (if there is a difference) and this is taken from the overall delay time. The new departure
time is calculated from this delay and compared with the original delay time. If a delay time threshold
is crossed, the care costs are multiplied by the number of passengers on that next flight.
Accommodation is also included in the care cost if a night-time threshold is reached. Equations 3 and
4 demonstrate the process in the model to determine if care and help costs need to be paid and if so by
how much, using IF functions.
A =IF((DPS + (DPS – (IS –IMIN)) > NT, "Yes", "No")
[3]
𝑇𝐶𝐻 = 𝐼𝐹(𝐴 = "𝑌𝑒𝑠", (𝐶𝐴 + 𝐶𝐻 ) ∗ 𝑃, 𝐼𝐹(𝐷𝑅 > 𝐷𝑇 , 𝐶𝐻 ∗ 𝑃, 0))
[4]
Where:
A = Overnight accommodation required
DPS = New departure time
IS = Scheduled interval between flights
IMIN = Minimum interval between flights i.e. fastest turnaround of the aircraft
NT = Night time threshold time
TCAH = Total cost of help, care and accommodation
CA = Cost of overnight accommodation
CH = Cost of care and help
P = Number of passengers
DR = Remaining delay after turnaround of aircraft
DT = Care and help delay time threshold
CH = Cost of care and help
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Rebooking passengers is slightly more complicated. Firstly it is calculated as to whether passengers
will miss their connecting flights given the information inputted on the interface page by the airline.
The departure time for the connecting flight is taken from the flight information page and compared to
the expected arrival time of the original aircraft given the expected delay. This gives the available
transfer time, which is compared against the minimum transfer time required by the passengers.
Whether the flight will be missed or not can then be determined (Equation 5).
𝑀𝐹 = 𝐼𝐹(((𝐷𝑃𝐶 − 𝐴𝑅𝑂 ) − 𝐼𝑆 ) > 0, No, Yes)
[5]
Where:
MF = Missed Flight
DPC = Scheduled departure time for connecting flight
ARO = Arrival time of original flight
IS = Scheduled interval between two flights
If the output is no, then no costs are incurred, if the output is yes then the same process is undertaken
for the next available flight and so on. If a flight has to be rebooked it is first determined whether the
flight is operated by the same airline as the original airline by searching for the identifier for that
airline in the flight code. If it is a flight operated by another airline then rebooking costs depending on
the class of passenger are multiplied by the number of passengers in that class.
The remaining parts of the model focus on the calculation of the optimum CI. A database of
flight Mach speeds is necessary to find the optimum speed. This data is taken from Piano-X [16]. This
is an aircraft analysis tool based on Piano, which is a widely used tool worldwide by airframe and
engine manufacturers, in major environmental studies and by the International Civil Aviation
Organisation (ICAO). Flight profiles can be created by adjusting performance characteristics, drag,
fuel consumption and environmental emission indices.
Using the number of passengers, cargo weight and the distance of the flight, a range of speeds
for the flight in questions can be calculated. Firstly the MRC of the flight is calculated from the
economy speed setting in Piano-X. This gives an output displaying flight time, fuel use and emissions
of the flight. Mach numbers at 0.001 increments are then inputted into Piano-X starting from the
MRC up to the maximum speed the aircraft is able to fly, with every flight time, fuel use and
emissions value taken for the individual speeds. The initial CI calculation takes the form of the
traditional CI calculation using data previously calculated in the preceding databases (Equation 6).
𝐶𝐼 =
𝐿𝐶 + 𝑀𝐶
𝐹𝐶
[6]
Where:
CI = Cost Index (kg/min)
LC = Labour Costs ($/min)
MC = Maintenance Costs ($/min)
FC = Fuel Costs ($/kg)
Once the CI is found it is used to find the Cost Function (CF) for each Mach number calculated by
using Equation 7. The Mach number for which the lowest CF is found i.e. where direct operating
costs are minimised is the desired flight profile that results from the calculated CI, giving the flight
time needed for further calculations.
𝐶𝐹 =
Where:
𝑓𝑓 + 𝐶𝐼
𝑉𝑔
[7]
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
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ff = fuel flow in kg/min
CI = in kg/min
Vg = Ground Speed which is the Mach (including addition of wind speed) multiplied by the speed of
sound at altitude.
The final part of the model is the optimisation of the CI. In total four different CI values are calculated
and the one that results in the lowest cost within the flight schedule is the one chosen as the optimum
CI value to use for the flight. The four CI values are as follows:
CI-1 The initial CI value calculated from the per-minute time-dependent costs and the fuel
costs per kilogram for that flight.
CI-2 A new CI is calculated if the flight time from CI-1 does not fit the schedule representing
the closest flight parameters that does meet schedule time.
CI-3 A recalculated CI taking into account delay, if present. This calculates any passenger
costs and overtime for crew or maintenance.
CI-4 If delay is present this recalculates the CI to make up as much of the delay as possible,
regardless of the total cost.
For the original CI-1 flight the cost of labour, maintenance and fuel are combined with the
additional costs of delay. Crew overtime costs are calculated by taking the hours available and
comparing them to the actual time of the flight with delay. If this number comes out positive i.e. more
time than the crew have available then the amount of overtime for the month is calculated for each
crew member. There are three categories for this: 84-90 hours at 1.5 times salary, 90-100 hours at 2.5
times salary and over 100 hours at 3.5 times salary.
For maintenance, the contracted hours or extra hours affecting flight maintenance schedules
are also calculated in a similar way. An exceedance of hours resulting in any penalty payments will
also be added to the cost. Passenger delay costs will also need to be added as described previously i.e.
compensation, help and care and the rebooking of passengers.
For the newly recalculated CI-3 and CI-4 values flight the costs are calculated in a similar
way but with smaller delay costs. For CI-4 this may mean no delay costs if all delay time can be made
up in-flight but when the delay is so significant that it cannot be accounted for in the schedule, even
with the fastest possible flight time, delay costs are applied to remaining delay time. This basically
assesses whether a faster flight to avoid delay is worth it when additional fuel costs are considered.
Once these total costs for the different CI values have been calculated the smallest total cost is
found and this is the CI that is displayed to the user on the interface page, along with the flight
characteristics e.g. fuel use, emissions, flight time etc.
4 RESULTS OF MODEL USE
Using current fuel prices and costs provided by a major international airline, a 10% increase in inputs
to the OCI model on the key outputs was undertaken to test the use of the model. It is evident that fuel
price and time-dependent costs have a very similar impact on all the outputs. The only slight variation
is in flight time where time costs have a slightly higher impact in decreasing flight time, although all
results are fairly negligible. As the CI balances extra delay, increasing it by 10% has no or very little
impact.
As CI is not linear the sensitivity of results depends on the base CI that is used. As seen in Figure 1
the higher the CI the greater effect changing it can have on outputs. The same analysis as previously
undertaken at a CI of 40 was performed with a base CI of 100. In this case, the impacts on fuel use,
flight time and emissions are still small, although higher than for CI=40. However, this time the
impact on total costs is more noticeable with fuel price having the greatest impact, followed by time
costs.
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
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In the sensitivity analysis the 10% increase in delay time was conducted from a low base of 15
minutes, therefore a 10% increase had very little impact. However, delay costs associated with
passenger compensation and care/help costs are unique in that specific delay time thresholds trigger
them. In the case of long haul flights this is at three and five hours. It is evident from Error!
Reference source not found. that the impact of these thresholds being passed is significant. When
there is any delay the alternate optimum CI is always favoured, although the difference between this
and the normal CI is marginal. However it is clear that once the three-hour threshold is passed, costs
are kept to a minimum by taking account of this extra delay, opposed to using the normal CI that
would cause total costs to spike dramatically.
However, it is very important to note that accounting for extra passenger delay costs does not mean
trying to recover all the delay time. This is also represented in Figure 4, showing that the total costs
are still higher than optimum CI and are still subject to the same thresholds as the normal CI value.
This is because this strategy of recovering delay does not include the additional costs of fuel that
result from such a substantial increase in speed caused by the significant increase in CI.
Figure 4: Impact of delay time on total costs and change in CO 2 emissions
However, there is also another complicating factor: the impact on CO2 emissions. In contrast to total
costs, the best scenario would be the one where the normal CI value is used. The optimum CI still
performs well compared to the normal CI until delay reaches around 120 minutes when the CO2
emissions start to increase. By far the worst scenario for CO2 is the one where all delay time is
recovered. This is partly to do with the fact that at present the emission of CO2 is not priced and
therefore in the CI equation it currently has no value. If a carbon price was to be added then this could
change the situation. However the highest carbon price projected by DECC [17] in 2050 is $124/kg.
Even with only a 15-minute delay a price double this would be needed to stop the CI from increasing.
As delay gets higher this number increases dramatically. At only 45 minutes the price needed would
be $11/kg, at 180 minutes $35/kg and at 300 minutes $100/kg. These latter prices for carbon are very
unrealistic; therefore this highlights the need to reduce delay in order to reduce carbon emissions as
well.
5
APPLICATION OF THE OCI MODEL
The aim of creating the OCI model is to make an accessible and transparent model for the calculation
of optimal CI for airlines. Excel is deliberately used for this purpose as it creates a more accessible
model with the steps involved in calculation easy to follow. By seeing that these kinds of calculations
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
12
can be done in this way may help to convince airlines that optimising the CI is something that can
easily incorporate into their flight planning systems. The use of Excel also makes the model easily
adaptable by airlines. The setup of the model means that on a day-to-day basis airline operations
would only need to use the interface page. However, adjustments to other parts of the model would
need to be made occasionally, such as the amount of fuel hedged and at what price, additional
connecting services, additional crew etc., although this is relatively easy to do.
Whilst the model effectively addresses the problems that exist with cumulative crew costs,
there are some costs that the airline may still find it hard to account for. For example, maintenance
costs are particularly problematic. Although the model does address the issue of maintenance
contracts, the initial maintenance costs may still not be known as discussed in section 3. It is
suggested that if maintenance costs cannot be determined by the airline, a good estimation to use
would be the costs for A and C checks as suggested by the University of Westminster Transport
Studies Group [14].
Delay costs represent one of the trickiest parts of the model, as it is so changeable even
throughout the flight. Delay management is already a part of some airline’s decision process. The OCI
model is flexible enough to accommodate an airlines own system of accounting for delay if necessary.
The only caveat with this is ensuring that airlines delay models actually take the balance of costs into
account, with extra fuel costs being considered as well as time dependent costs.
There is also the option of airlines using a basic version of the OCI model, which has the
same features of the OCI model, but with a slimmed down delay cost calculation. These delay costs
are taken from the University of Westminster Transport Studies Group [18] who have done extensive
work in this area and include pre-set values for different delay categories (e.g. 1-15 minutes, 16-30
minutes etc.). This means that airlines do not need to include the connecting flights of passengers,
which may be more time consuming. However, this method should be used with caution as these costs
are not airline specific and therefore are only a rough estimate compared to the advanced OCI model.
Whilst this model does provide a significant improvement on the current system of CI
calculation, there are still areas that could be improved upon. Firstly the Piano-X calculations are time
consuming as each Mach number has to be generated individually. Using average passenger numbers
and cargo loads for the flight in question could solve this. However, it should be noted that Piano-X is
free software whereas most airlines have more sophisticated flight analysis software at their disposal.
Therefore, this could be integrated into the system to optimise calculations.
Another issue is the amount of data potentially needing to be held in the worksheet for flights,
crew members and aircraft. Multiple copies of the model can be created for different flights, which
may overcome the problem. However, more powerful computing software may be needed in the
future to accommodate data demands. This will ultimately depend on the individual airline using the
model.
Even though these issues need to be addressed, it should be noted that if the assertion by
Burrows et al. [10] that “relatively crude approaches are likely to be cost effective” is correct then the
model still has significant value even when inputs may not be 100% accurately known by the airline
e.g. good estimation of maintenance costs would be sufficient.
Going forward the model will also be used as part of on-going research into the effects of policy
on flights costs and emissions. This adds additional value to the OCI model, making it not just of use
to airlines but also to policy makers and airline authorities.
6
CONCLUSION
With rising fuel costs and climate change concerns, the optimisation of the CI calculation is vital. To
date there has been a general issue amongst airlines with the misuse or miscalculation of CI values
which has led to the practice of sub-optimal CI values being used.
Many airlines have expressed an interest in correcting this as they begin to appreciate the
value of CI in optimising costs. Therefore the aim of this research was to create a new model for the
calculation of the optimum CI. The OCI model looks to break out of the assertion that the calculation
must take place within the constraints of traditional CI equation and instead proposes that complex
cost factors should be dealt with in an alternative way. The OCI does use the CI equation as a basis
H.A. Edwards, D. Dixon-Hardy & Z. Wadud
13
for the initial CI calculation, but then relies on an assessment of whether the flight can be achieved in
a scheduled time, including delay. If not then further calculations can be made that take into account
any additional costs to achieve this flight with the current CI, such as cumulative crew costs, extra
maintenance costs and the cost of passenger delay and compare those with the cost of flying at a CI
which will result in a faster flight, within schedule.
The OCI model which has been created has shown that these calculations can be conducted in
this way with a simple to use interface for airline operations departments. Further adaptation of the
model could take place with, for example, airlines integrated their own flight analysis software to
increase its functionality. But the basic premise of the model provides evidence that optimisation of
CI can take place in an efficient manner that is neither costly nor time consuming.
In addition to developing this model as a tool for airlines, the model will also be used in
future research to assess the impact of changing costs and policy on a flight-by-flight basis. This will
particularly focus on the potential introduction of a carbon price, as well as an increase in fuel prices
in the future. This adds value to the OCI model as it can not only be of benefit to airlines, but also to
policy makers and aviation authorities.
ACKNOWLEDGEMENT
This work was financially supported by the Engineering and Physical Sciences Research Council
through the University of Leeds Doctoral Training Centre in Low Carbon Technologies.
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